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Arithmetic with Modular Numbers: Applying Congruences Online Quiz Questions

Use this free practice quiz with 20 questions to review Arithmetic with Modular Numbers: Applying Congruences, test your knowledge, and prepare for your next test or exam.

20 questions
01
Choose one
1 point

Which statement is equivalent to a ≡ b modulo m?

  1. A

    a is divisible by b

  2. B

    m divides a minus b

  3. C

    a and b are exactly equal

  4. D

    a plus b is divisible by m

02
Choose one
1 point

What is the least nonnegative remainder when 47 + 38 is divided by 6?

  1. A

    1

  2. B

    2

  3. C

    5

  4. D

    7

03
Choose one
1 point

What is the least nonnegative remainder of (26 + 41) × 13 when divided by 7?

  1. A

    0

  2. B

    1

  3. C

    3

  4. D

    6

04
Choose all
1 point

Select all numbers that are congruent to 4 modulo 7.

  1. A

    11

  2. B

    18

  3. C

    25

  4. D

    30

05
Choose all
1 point

Suppose a ≡ r modulo m and b ≡ s modulo m. Select all conclusions that are always justified by the modular arithmetic rules in the material.

  1. A

    a + b ≡ r + s modulo m

  2. B

    a − b ≡ r − s modulo m

  3. C

    ab ≡ rs modulo m

  4. D

    a ÷ b ≡ r ÷ s modulo m in every case

06
True or false
1 point

True or false: The statement 17 ≡ 3 modulo 7 means that 17 and 3 are exactly equal.

  1. A

    True

  2. B

    False

07
True or false
1 point

True or false: From 2x ≡ 2 modulo 6, one may automatically conclude that x ≡ 1 modulo 6.

  1. A

    True

  2. B

    False

08
Written response
1 point

What is the least nonnegative remainder when 92 − 57 is divided by 8?

09
Written response
1 point

If x ≡ 3 modulo 7, what is the least nonnegative remainder of x + 18 modulo 7?

10
Fill in the blank
1 point

Complete both statements: a ≡ b modulo m exactly when . When dividing by the positive integer m, the possible remainders are .

11
Fill in the blank
1 point

Complete the calculation: The least nonnegative remainder of −7 modulo 12 is . This can be found by subtracting the remainder of 7 from .

12
Open ended
1 point

Find the remainder of x modulo 7 if 2x + 3 ≡ 1 modulo 7. Explain your reasoning and verify the result.

13
Choose one
1 point

What is the remainder when 10^20 + 5 is divided by 10?

  1. A

    0

  2. B

    1

  3. C

    4

  4. D

    5

14
Choose one
1 point

What is the least nonnegative remainder when 74 + 53 is divided by 9?

  1. A

    1

  2. B

    2

  3. C

    3

  4. D

    4

15
True or false
1 point

True or false: The statement 17 is congruent to 3 modulo 7 means that 17 and 3 are exactly equal.

  1. A

    True

  2. B

    False

16
Choose one
1 point

What is the least nonnegative remainder when 23 − 58 is divided by 11?

  1. A

    9

  2. B

    8

  3. C

    10

  4. D

    1

17
Written response
1 point

If x is congruent to 6 modulo 8, what is the least nonnegative remainder of 3x + 5 modulo 8?

18
Choose one
1 point

What is the least nonnegative remainder of 47 × 26 modulo 7?

  1. A

    2

  2. B

    4

  3. C

    5

  4. D

    6

19
Written response
1 point

If n + 17 is congruent to 4 modulo 12, what is the least nonnegative remainder of n modulo 12?

20
Choose one
1 point

What is the least nonnegative remainder of (39 + 68) × 14 modulo 10?

  1. A

    2

  2. B

    4

  3. C

    6

  4. D

    8